Bifurcations and Hopf degeneracies in nonlinear feedback systems with time delay

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 6, Issue 4, 1996, Pages 661-672

  Moiola, Jorge L ^a   Chiacchiarini, Héctor G ^c   Desages, Alfredo C ^b  

^a UNIVERSIDAD NACIONAL DEL SUR   (Argentina)

^b Universidad Provincial del Sudoeste   (Argentina)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039120726     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127496000333     Document Type: Article

References (31)

1. Barmish, B. R. & Shi, Z. [1989] "Robust stability of perturbed systems with time delays," Automatica 25, 371-381.
2. Bélair, J. & Campbell, S. A. [1994] "Stability and bifurcations of equilibrium in a multiple-delayed differential equation," SIAM J. Appl. Math. 54, 1402-1424.
3. Beuter, A., Bélair, J. & Labrie, C. [1993] "Feedback and delays in neurological diseases: A modelling study using dynamical systems," Bull. of Math. Biol. 55, 525-541.
4. Boe, E. & Chang, H. -C. [1991] "Transition to chaos from a two-torus in a delayed feedback system," Int. J. Bifurcation and Chaos 1, 67-81.
5. Brierley, S. D., Chiasson, J. N., Lee, E. B. & Zak, S. H. [1982] "On stability independent of delay for linear systems," IEEE Trans. Automat. Contr. AC-27, 252-254.
6. Chow, S. -N., Hale, J. K. & Huang, W. [1992] "From sine waves to square waves in delay equations," Proceedings of the Royal Society of Edinburgh, Sec. A - Mathematics 120, pp. 3-4, 223-229.
7. Colantonio, M. C., Padín, M., Desages, A. C. & Romagnoli, J. A. [1991] "Application of higher-order bifurcation formulas," IEEE Trans. Automat. Contr. AC-36, 746-749.
8. Edmunds, J. M. [1979] "Characteristic gains, characteristic frequencies and stability," Int. J. Contr. 29, 669-706.
9. Fu, M., Olbrot, A. W. & Polis, M. P. [1989] "Robust stability for time-delay systems: The edge theorem and graphical tests," IEEE Trans. Automat. Contr. 34, 813-820.
10. Hale, J. K. [1991] "Dynamics and delays," in Delay Differential Equations and Dynamical Systems, eds. Busenberg, S. & Martelli, M. (Springer-Verlag) pp. 16-29.
11. Hale, J. K. & Huang, W. [1993] "Global geometry of the stable regions for two delay differential equations," J. Math. Anal. Appl. 178, 344-362.
12. Hamada, N. & Anderson, B. D. O. [1983] "Simplified stability tests for delay-differential systems," IEEE Trans. Circ. Syst. CAS-30, 488-492.
13. Hassard, B. D. & Wan, Y. H. [1978] "Bifurcation formulae derived from center manifold theory," J. Math. Anal. Appl. 63, 297-312.
14. Kamen, E. W. [1982] "Linear systems with commensurate time delays: Stability and stabilization independent of delay," IEEE Trans. Automat. Contr. AC-27, 367-375.
15. Kwatny, H. G. & Piper, G. E. [1990] "Frequency domain analysis of Hopf bifurcation in electric power networks," IEEE Trans. Circ. Syst. CAS-37, 1317-1321.
16. Lee, T. N. & Dianat, S. [1981] "Stability of time-delay systems," IEEE Trans. Automat. Contr. AC-26, 951-953.
17. MacFarlane, A. G. J. & Postlethwaite, I. [1977] "The generalized Nyquist stability criterion and the multivariable root loci," Int. J. Contr. 25, 81-127.
18. Manitius, A. Z. & Olbrot, A. W. [1979] "Finite spectrum assignment problem for systems with delays," IEEE Trans. Automat. Contr. AC-24, 541-553.
19. Manitius, A. Z. [1984] "Feedback controllers for a wind tunnel model involving a delay: Analytical design and numerical simulation," IEEE Trans. Automat. Contr. AC-29, 1058-1068.
20. Mees, A. I. & Allwright, D. J. [1979] "Using Characteristic loci in the Hopf bifurcation". Proc. Instn. Elect. Engrs. 126, 628-632.
21. Mees, A. I. & Chua, L. O. [1979] "The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems," IEEE Trans. Circ. Syst. CAS-26, 235-254.
22. Mees, A. I. [1981] Dynamics of Feedback Systems (Chichester: John Wiley & Sons).
23. Moiola, J. L., Castro, L., Cendra, H. & Desages, A. C. [1990] "Degenerate bifurcations and catastrophe sets via frequency analysis," Dynamics and Stability of Systems 5, 163-181.
24. Moiola, J. L. [1993] "On the computation of local bifurcation diagrams near degenerate Hopf bifurcations of certain types," Int. J. Bifurcation and Chaos 3, 1103-1122.
25. Moiola, J. L. & Chen, G. [1993a] "Computation of limit cycles via higher-order harmonic balance approximation," IEEE Trans. Automat. Contr. 38, 782-790.
26. Moiola, J. L. & Chen, G. [1993b] "Frequency domain approach to computation and analysis of bifurcations and limit cycles: A tutorial," Int. J. of Bifurcation and Chaos 3, 843-867.
27. Rodet, X. [1993] "Models of musical instruments from Chua's circuit with time delays," IEEE Trans. Circ. Syst. - Part II - Analog and Digital Signal Processing 40, 696-701.
28. Suh, H. H. & Bien, Z. [1982] "A root-locus technique for linear systems with delay," IEEE Trans. Automat. Contr. AC-27, 205-208.
29. Thowsen, A. [1981] "An analytic stability test for a class of time-delay systems," IEEE Trans. Automat. Contr. AC-26, 735-736.
30. Utkin, V. I. [1977] "Variable structure systems with sliding modes," IEEE Trans. Automat. Contr. AC-22, 212-222.
31. Watanabe, K., Nobuyama, E., Kitamori, T. & Ito, M. [1992] "A new algorithm for finite spectrum assignment of single-input systems with time delay," IEEE Trans. Automat. Contr. AC-37, 1377-1383.